Statistics Calculator
Paste any data (even from Excel) โ full panel: mean/median/mode, sample & population SD, quartiles, outliers, histogram, box plot & PDF.
15 values recognised
81.4
Mean
83
Median
85
Mode
8.9905
Std dev (s)
33
Range
15
Count
๐ Distribution
Histogram with 5 bins (Sturges' rule).
๐ฆ Five-number summary
Box plot: min ยท Q1 ยท median ยท Q3 ยท max, dots = outliers beyond 1.5รIQR.
Min
62
Q1
77.5
Median
83
Q3
86.5
Max
95
๐ The full panel โ sample vs population
Use sample statistics (รท nโ1) when your data is a sample of a larger group โ the usual case in homework. Population (รท n) applies when the data IS the whole group.
๐ก Quartiles use linear interpolation (the Excel QUARTILE.INC method). Some textbooks use exclusive variants โ if your course prescribes one, tiny differences at Q1/Q3 are expected.
๐Paste your data, get the whole panel
Drop in any list of numbers โ commas, spaces, or a column straight from Excel โ and get every descriptive statistic your course asks for at once: mean, median, mode(s), quartiles with IQR, range, variance and standard deviation in both sample and population versions (the distinction homework loses marks over), standard error, coefficient of variation, and automatic outlier detection by the 1.5รIQR rule โ visualised with a live histogram and box plot, exportable as a PDF report.
๐Everything you'd want to know
- Forgiving input: commas, spaces, semicolons, new lines, Excel columns โ non-numeric tokens are counted and skipped, never silently mangled.
- All modes reported when there's a tie; 'no mode' stated honestly when nothing repeats.
- Sample (รท nโ1) and population (รท n) variance & SD side by side, with guidance on which to use.
- Five-number summary as a real box plot, with outliers drawn as dots beyond the whiskers.
- A histogram binned by Sturges' rule, a copy-everything button, and a branded PDF report.
๐งฎThe formulas
The nโ1 in sample variance (Bessel's correction) compensates for estimating the mean from the same data โ samples systematically underestimate spread without it. Quartiles use linear interpolation, matching Excel's QUARTILE.INC and most statistics packages.
๐กReading your results
- Mean far from median? Your data is skewed โ report the median and say why.
- CV lets you compare spread across different units: a 10% CV in marks vs a 25% CV in study hours.
- SEM shrinks with sample size โ it measures how well you know the mean, not how spread the data is.
- Outliers deserve investigation, not automatic deletion: they're either errors or the most interesting data points.
๐ก Frequently Asked Questions
How do I find mean, median, and mode?+
Mean = sum รท count; median = the middle value once sorted (average of the two middles for even counts); mode = the most frequent value(s). Paste your numbers and all three appear instantly with the rest of the panel.
What is the difference between sample and population standard deviation?+
Sample SD divides by nโ1 (Bessel's correction), population SD by n. Use sample when your data represents a bigger group โ the usual homework case; use population when the data is the entire group. This calculator shows both, labelled.
How are outliers detected?+
By the standard 1.5รIQR rule: anything below Q1 โ 1.5รIQR or above Q3 + 1.5รIQR is flagged and drawn as a dot outside the box plot's whiskers. The fences adapt to your data's own spread.
What if my data has two modes?+
The calculator reports every value tied for the highest frequency โ bimodal and multimodal sets are shown in full, and 'no mode' is stated when nothing repeats (rather than inventing one).
Can I paste data from Excel or Google Sheets?+
Yes โ copy a column or row and paste directly. The parser accepts newlines, tabs, commas, spaces, and semicolons, tells you how many values it recognised, and counts anything non-numeric it had to skip.
What is IQR and why does it matter?+
The interquartile range (Q3 โ Q1) spans the middle 50% of your data. Unlike range, it ignores extremes, which makes it the robust choice for describing spread โ and the basis of the outlier fences.